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Abstract

Recent work [1] and [2] has demonstrated an operating signature verification system based on the motion of the stylus during the signature as measured by two accelerometers. This work tacitly assumed that the motion of the pen point could be determined by means of a tablet or a pair of accelerometers mounted within the pen.

Country

United States

Language

English (United States)

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Signature Verification Based on Complete Accelerometry

Recent work [1] and [2] has demonstrated an operating signature verification
system based on the motion of the stylus during the signature as measured by
two accelerometers. This work tacitly assumed that the motion of the pen point
could be determined by means of a tablet or a pair of accelerometers mounted
within the pen.

Measurements on a large number of actual signatures has revealed that
many signatures contain substantial rotational or pitching motions, as well as
pure translations. Thus a complete description of the pen motion must include
rotations of the pen about the point (pitch) as well as translations.

The practical importance of this became clear when several individuals were
observed writing almost exclusively with finger motions, by rocking the pen back
and forth. The two-accelerometer pen gave no output for these signatures,
although the motions were appreciable.

By classical mechanics, the complete description of a rigid body in 3-space
requires 6 measurements. Some simplifications are possible because of the
nature of the signature. Fig. 1 shows the pen schematically located in space.
Accelerometers are mounted at A and B. The acceleration q at any point on the
pen is given by the well-known equation q = w x r + wx(wxr) + Lambda/-1/ (f + g)
where f is the translational force of the pen origin in space coordinates, g is the
force of gravity, r the location of q relative to the pen origin, and Lambda is the
transformation from body to space coordinates. The essence of this structure is
to use f and w, or approximations thereto, as measurements for signature
verification.

A six accelerometer pen is not overly practical. Since the pen is in contact
with the writing surface and axial rotations of the pen appear to be very
significant, the disclosed system has only four important degrees of freedom.
Thus four accelerometers yield a useful approximate solution.

Such a pen is shown in Fig. 2. Four miniature semiconductor
accelerometers 12, 0.125 in. diameter, are mounted in parallel tubes
symmetrically placed about the pen axis. The pen also contains a pressure
gauge 14. As shown, the pen is a ball-point pen with an ink cartridge 16. The
pen is approximately 1/2'' in diameter. The necessary wires leading from the
pen's five individual sensing elements are not shown. General form

In its most general form, the pen must contain 6 noncolinear accelerometers.
The 6 accelerations are then processed along classical lines of inertial navigation [3]. 1. Determine [w] algebraically. 2. Integrate to find [w]. 3. Solve the ordinary
differential equation Lambda = Lambda w for the direction cosines. 4. Solve the
remaining 3 equations for [g + f]. The initial conditions can be determined by
tracking the pen from its re...